A lateral seal of this type is disclosed in WO 2004/033130, FIGS. 7 to 9. It comprises a wetted first part made from a fireproof material and a second part made from a high-temperature-resistant material that is allocated to the front sides of the casting rollers. The second part has a kind of “snout shape” with two legs which extend along the casting roller front sides and join together at the bottom above a so-called kissing point to form a common area, between which legs the first part protrudes from above. The first part is made from a fireproof material, the second from a high-temperature-resistant alloy, a grey cast iron or a high-strength steel. The two parts are provided with a coating.